Method for removing spatial and temporal multi-path interference for a receiver of frequency-modulated radio signals

ABSTRACT

A method for decreasing multi-path interference, for a vehicle radio receiver including at least two radio reception antennas that each receive a plurality of radio signals composed of time-shifted radio signals resulting from a multi-path effect. The plurality of radio signals combined to deliver a combined radio signal y s  to be played, with: y n =W n   T [ G 1,n   S   , X 1,n + G 2,n   S   , X 2,n  ] at time n, where x 1  and x 2  are vectors the components of which correspond to the plurality of signals received by the first antenna and by the second antenna, respectively, G 1,n   S  and G 2,n   S  are scalars the components of which are the complex weights of a spatial filter and w n   T  is the transpose matrix of a vector the components of which are the complex weights of a temporal filter. The method includes implementation of an iterative adaptation algorithm to determine the complex weights of the spatial filter and the complex weights of the temporal filter.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is the U.S. National Phase Application of PCTInternational Application No. PCT/FR2018/051249, filed May 31, 2018,which claims priority to French Patent Application No. 1754868, filedJun. 1, 2017, the contents of such applications being incorporated byreference herein.

FIELD OF THE INVENTION

The invention relates to the field of the reception offrequency-modulated radio signals, in particular in mobile radioreceivers exposed to the effect of multi-paths, which is known to thoseskilled in the art.

More precisely, the present invention relates to a method for removingreflected radio waves resulting from the multi-path effect in a receiverof frequency-modulated radio signals, by means of both spatial andtemporal processing of this interference.

BACKGROUND OF THE INVENTION

As is known, a radio receiver, in particular in a multimedia system of amotor vehicle, is able to receive a radio signal, in particular an FMradio signal, FM being the acronym of “frequency modulation”.

Such an FM radio signal, received in modulated form by a radio receiver,is subjected to various sensors and to suitable filtering so that thecorresponding demodulated radio signal is able to be played back undergood conditions, in particular in the passenger compartment of a motorvehicle.

Those skilled in the art know the operating principle of an FM, that isto say frequency-modulated, radio signal received by a suitable radioreceiver, with a view to being demodulated and then played to listeners.

A known problem that relates to the reception of an FM radio signal viaa mobile radio receiver, in particular one incorporated into a motorvehicle, resides in the fact that the FM radio signal emitted by anemitter may be reflected by natural obstacles or buildings for example,before being received by an antenna of the radio receiver. In otherwords, the emitted radio signal, before being received by an antenna ofthe receiver, may have followed various paths, of relatively long orshort length. The emitted signal may furthermore, because of masking,not be received at all by the antenna of the radio receiver.

As a result thereof a selectivity is necessary, because a given radiosignal may be received by one antenna several times, with various timeshifts. This problem is known to those skilled in the art, who generallyrefer to it as “multi-path”.

In addition, to mitigate the aforementioned drawbacks relative tomulti-path and masking, it is known to equip radio receivers with atleast two separate antennas that are said to create “phase diversity”.

Phase-diversity systems comprising two antennas are one known solutionto the problem of generating frequency selectivity with a view toprocessing interference due to multi-path in motor-vehicle radioreceivers.

The principle consists in combining the FM radio signals received by twoseparate antennas of a radio receiver, in order to make, virtually, theassembly formed by said two antennas directional, in order to privilegea desired radio signal reaching the antenna array at a certain angle, tothe detriment of an undesired radio signal reaching the antenna networkat a different angle.

To mitigate the effect of the spatial and temporal interference inducedby the multi-path effect, systems for achieving channel equalization bymeans of a specific configuration of an impulse response filter (alsoreferred to as an “FIR”) exist, in order to equilibrate the transferfunction of the channel.

In this prior art, multi-tuner receivers thus employ two types ofprocessing, which are carried out separately, the spatial processingwith “phase diversity” being carried out upstream of the temporalequalization of the channel.

Furthermore, in the prior art, algorithms for removing multi-pathsignals are generally of the “constant modulus” type. Specifically, theprinciple of frequency modulation ensures that the emitted radio signalhas a constant modulus. Thus, computational algorithms called constantmodulus algorithms (CMAs) have been developed and those skilled in theart are constantly seeking to improve them, with for main constraint toensure, after computation, a substantially constant modulus of the radiosignal combined within the receiver, after processing.

CMA algorithms are iterative computational algorithms the objective ofwhich is to determine the real and imaginary parts of complex weights tobe applied to the FM radio signals received by one or more antennas of aradio receiver, with a view to combining them, so as to remove from thecombined radio signal the interference due to multi-path.

It is therefore a question, in the prior art, of determining thecomponents of a spatial filtering, by means of a first implementation ofa CMA algorithm, then the components of an impulse response filter, forthe temporal filtering, by means of the implementation of a second CMAalgorithm.

FIG. 1 shows a schematic representative of the prior art, in which twoantennas A1, A2 respectively receive radio signals X_(1,n), X_(2,n)corresponding to an emitted FM radio signal, via respective input stagesFE1, FE2. Two successive filtering stages are implemented to achieve therecombined signal Yn intended to be played. Firstly, there is a spatialfiltering stage G1 and G2, respectively, then a temporal filtering stageW.

With reference to FIG. 1, a first set of equations of a system with“spatial diversity” results there from:

z _(n)=G_(1,n) ^(s) , X _(1,n) + G_(2,n) X _(2,n)

J _(CMA) =E{(|z _(n) |−R)²}

where G_(1,n) ^(s), G_(2,n) ^(s) are scalars of complex weights, for thespatial filtering of the signals X_(1,n), X_(2,n) received by each ofthe antennas A1, A2; J_(CMA) is the cost function to be minimized bymeans of a CMA algorithm and R is a constant to be determined,corresponding to the constant modulus of the combined signal.

A second set of equations of a system with “temporal diversity” resultsthere from:

y_(n)=(W _(n) ^(t))^(T) Z _(n)

J _(CMA) ,=E{(|y _(n) |−R)²}

where W_(n) ^(t) is a matrix of complex weights the components of whichcorrespond to the coefficients of an impulse response filter to beapplied to the signal Z_(n) for the temporal filtering, Z_(n) beingcomposed of successive samples of the signal z_(n) issued from thespatial filtering stage; J_(CMA), is the cost function to be minimizedby means of a CMA algorithm and R is a constant to be determined,corresponding to the constant modulus of the combined signal.

However, as the spatial filtering is performed upstream andindependently, i.e. without taking into account the time dimension ofthe interference, problems arise. Specifically, a first iterative CMAalgorithm is implemented for the spatial filtering. The fact that thetime issue is not taken into account at this stage means that theimplemented algorithm may at any moment hop to an adjacent radio signal.The temporal filtering performed subsequently may then have substantialdifficulty converging, or even not converge.

The high number of unknowns and the absence of correlation between theseunknowns makes rapid determination of stable solutions particularlydifficult.

As is known to those skilled in the art, this difficulty with rapidlyconverging to correct and stable solutions is particularly present inthe field of FM radio reception, because the only certain constraintexploitable a priori by algorithms resides in the fact that the modulusof the envelope of the frequency-modulated radio signal remainsconstant.

However, on the other hand, the antennas A1, A2 each receive a pluralityof radio signals, corresponding to the emitted radio signal havingfollowed various paths, which are either direct or with one or morereflections, and a complex weight must be determined with a view tobeing applied to each of these radio signals. The equation contains ahigh number of unknowns and the objective of the CMA algorithms istherefore to determine the best solutions, among a set of non-optimalsolutions allowing a constant modulus of the combined radio signal to beensured.

More particularly, in scenarios where the desired radio signals coexistwith radio signals transmitted over adjacent frequency channels, thisproblem of convergence is more pronounced. It often occurs that thecomplex weights obtained with CMA algorithms privilege adjacent radiosignals to the detriment of the desired radio signals. Stabilityproblems are thus particularly frequent.

SUMMARY OF THE INVENTION

To remedy these drawbacks, an aspect of the present invention proposes,firstly, to perform a single spatial and temporal optimization afterlinear combination of all of the signals received by at least twoantennas that are separate from one another.

A single iterative algorithm, in particular of CMA type, is thusimplemented to carry out both the spatial filtering and the temporalfiltering for the plurality of signals received by said at least twoseparate antennas.

Secondly, according to one preferred embodiment, the obtained equationis translated into polar coordinates in order to introduce a physicalsense in the form of a relationship between the signals received by saidat least two antennas. Advantageously, with respect to the prior art,this solution allows orthogonal solution axes to be obtained for the CMAalgorithm implemented. In addition, by virtue of the correlationintroduced between the variation in the various coefficients, as isdemonstrated in the rest of the description, the capacity of theimplemented algorithm to rapidly converge to a small number of stablesolutions is moreover improved.

More precisely, one aspect of the present invention is a method fordecreasing multi-path interference, for implementation thereof in avehicle radio receiver, said radio receiver being intended to receive anemitted radio signal and comprising at least two radio receptionantennas that each receive a plurality of radio signals corresponding tosaid emitted radio signal, each of said plurality of signals received byeach of said antennas being composed of time-shifted radio signalsresulting from a multi-path effect, said plurality of radio signalsbeing combined to deliver a combined radio signal y_(n) to be played,with y_(n)=W_(n) ^(T)[G_(1,n) ^(T) , X_(1,n)+G_(2,n) ^(s) , X_(2,n)] atthe time n, where X₁ is a vector the components of which correspond to aplurality of signals received by a first antenna, expressed in complexbaseband, X₂ is a vector the components of which correspond to theplurality of signals received by a second antenna, expressed in complexbaseband, G_(1,n) ^(s) and G_(2,n) ^(s) are scalars the components ofwhich are the complex weights of a spatial filter and W_(n) ^(T) is thetranspose matrix of a vector the components of which are the complexweights of a temporal filter, said method comprising the implementationof an iterative adaption algorithm to determine said complex weights ofthe spatial filter and said complex weights of the temporal filter.

By virtue of the method according to an aspect of the invention, theiterative adaptation algorithm implemented to carry out the spatial andtemporal filtering of the plurality of radio signals received by said atleast two antennas converge more rapidly and more stably.

Advantageously, the iterative adaptation algorithm is configured tominimize a cost function J such that

J=E{(|y _(n) |−R)²}

where R is a constant to be determined, corresponding to the constantmodulus of the combined signal y_(n).

Advantageously, said iterative adaptation algorithm is a constantmodulus adaptation algorithm configured to minimize the cost function.

According to the preceding embodiment, the respective variations in thecomponents of the matrix the components of which form the complexweights of the temporal filter and in the components of the scalars thecomponents of which form the complex weights of a spectral filter arewritten:

$W_{n + 1}^{t} = {W_{n}^{t} - {\mu_{W}\frac{{y_{n}} - R}{y_{n}}{\overset{\_}{y_{n}}\left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}}}$$G_{1,{n + 1}}^{s} = {G_{1,n}^{s} - {\mu_{G\; 1}\frac{{y_{n}} - R}{y_{n}}{\overset{\_}{y_{n}}\left( \overset{\_}{W_{n}^{T}} \right)}^{T}} + X_{1,n}}$$G_{2,{n + 1}}^{s} = {G_{2,n}^{s} - {\mu_{G\; 2}\frac{{y_{n}} - R}{y_{n}}{\overset{\_}{y_{n}}\left( \overset{\_}{W_{n}^{T}} \right)}^{T}} + X_{2,n}}$

where μ_(W), μ_(G1), and μ_(G2) are iterative steps chosen for theupdate of the gains and phases of each of the complex weights.

In this embodiment, the high correlation that exists between thecomponents of the spatial filter and of the temporal filter means thatthe iterative adaptation algorithm is more efficient.

The preceding equations are generic and may be developed in cartesian orpolar coordinates. For an optimal efficiency, as is explained below,according to one preferred embodiment, the complex weights are expressedin polar coordinates.

According to this embodiment, the method according to an aspect of theinvention moreover comprises introducing a correlation between saidcomplex weights of the temporal filter and said complex weights of thespatial filter, said correlation being dependent on the time shiftbetween said plurality of radio signals received by said at least twoantennas, by means of the expression of said complex weights in polarcoordinates, so that the instantaneous gradient of the cost function iswritten:

${\nabla J} = {2{\frac{{y_{n}} - R}{y_{n}}\begin{bmatrix}{{Re}\left\lbrack {\overset{\_}{y_{n}}{e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}{A_{n}^{t} \circ e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack}} \\{{Re}\left\lbrack {\overset{\_}{y_{n}}{e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}b_{1,n}{e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack}} \\{{Re}\left\lbrack {\overset{\_}{y_{n}}{e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}b_{2,n}{e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack}}\end{bmatrix}}}$ with:W_(n)^(t) = A_(n)^(t) ∘ e^(−j θ_(n)^(t)), with:A_(n)^(t) = [a_(0, n)a_(1, n)a_(2, n)  …  a_(K − 1, n)]^(T)θ_(n)^(t) = [e^(−j θ_(0, n))e^(−j θ_(1, n))e^(−j θ_(2, n))  …  e^(−j θ_(K − 1, n))]^(T), and:G_(1, n)^(s) = b_(1, n)e^(−j ϕ_(1, n))G_(2, n)^(s) = b_(2, n)e^(−j ϕ_(2, n))

so as to incorporate an interdependence between the real and imaginaryparts of said complex weights.

According to the preceding embodiment, the respective variations in thecomponents of the matrix the components of which form the complexweights of the temporal filter and in the components of the scalars thecomponents of which form the complex weights of a spatial filter arewritten:

$A_{n + 1}^{t} = {A_{n}^{t} - {\mu_{A}\frac{{y_{n}} - R}{y_{n}}{{Re}\left\lbrack {\overset{\_}{y_{n}}{e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack}}}$$\theta_{n + 1}^{t} = {\theta_{n}^{t} + {\mu_{\theta}\frac{{y_{n}} - R}{y_{n}}{{Im}\left\lbrack {\overset{\_}{y_{n}}{A_{n}^{t} \circ e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack}}}$$b_{1,{n + 1}} = {b_{1,n} - {\mu_{b\; 1}\frac{{y_{n}} - R}{y_{n}}{{Re}\left\lbrack {\overset{\_}{y_{n}}{e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack}}}$$\phi_{1,{n + 1}} = {\phi_{1,n} + {\mu_{\phi \; 1}\frac{{y_{n}} - R}{y_{n}}{{Im}\left\lbrack {\overset{\_}{y_{n}}b_{1,n}{e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack}}}$$b_{2,{n + 1}} = {b_{2,n} - {\mu_{b\; 2}\frac{{y_{n}} - R}{y_{n}}{{Re}\left\lbrack {\overset{\_}{y_{n}}{e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack}}}$$\phi_{2,{n + 1}} = {\phi_{2,n} + {\mu_{\phi \; 2}\frac{{y_{n}} - R}{y_{n}}{{Im}\left\lbrack {\overset{\_}{y_{n}}b_{2,n}{e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack}}}$

where μ_(A), μ_(θ), μ_(b1), μ_(b2), μ_(φ1), μ_(φ2) are iterative stepschosen for the update of the gains and phases of each of the complexweights, and the operator “º” is defined as carrying out themultiplication of two vectors, component by component, the resultantbeing a vector.

In this embodiment, the very high correlation that exists between thecomponents of the spatial filter and of the temporal filter means thatthe iterative adaptation algorithm is more efficient.

Advantageously, the temporal filter is an impulse response filter.

An aspect of the present invention also relates to a radio receivercomprising a microcontroller configured to implement the method such asbriefly described above.

An aspect of the present invention also relates to a motor vehiclecomprising a radio receiver such as briefly described above.

BRIEF DESCRIPTION OF THE DRAWINGS

An aspect of the invention will be better understood on reading thefollowing description, which is given solely by way of example, withreference to the appended drawing, in which:

FIG. 1 shows the conceptual diagram of a method for cancelling outmulti-path radio signals, according to the prior art;

FIG. 2 shows the conceptual diagram of a method for cancelling outmulti-path radio signals, according to an aspect of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The method for adapting an FM radio signal according to an aspect of theinvention is presented with a view to an implementation, principally, ina radio receiver of a multimedia system on board a motor vehicle.However, an aspect of the present invention may also be implemented inany other technical field, and in particular in any type of FM radioreceiver.

An aspect of the present invention proposes to introduce an adaptivespatial and temporal model, in order to take into account both thespatial correlation and the temporal correlation that exists, from thephysical point of view, between the multi-path FM radio signals receivedby a plurality of antennas of the radio receiver in question.

It is known, in another technical field relative to radars, to use anadaptive temporal model to combine the signals received by a radarantenna. The techniques implemented in the field of radars is howevernot transposable as such to the field of FM radio reception.

The adaptive temporal model implemented in the world of radars is basedon the implementation of an impulse response filter able to apply, tothe vector of received complex signals, a complex weight vector that iswritten:

${Wn} = \begin{bmatrix}{\exp \left( {j\; 2\pi \; F_{d}0T} \right)} \\{\exp \left( {j\; 2\pi \; F_{d}1T} \right)} \\\vdots \\{\exp \left( {j\; 2\pi \; {F_{d}\left( {K - 1} \right)}T} \right)}\end{bmatrix}$

This model does not allow multi-path signals to be removed in the fieldof FM radio reception because each path followed by each of thetime-shifted, received multi-path signals has, in the case of an FMradio signal, a specific gain that is dependent on the distancetravelled by the radio wave, said distance not being a linearfrequency-dependent function, contrary to the case of radar reception.

In addition, this model does not allow the spatial correlation thatexists between signals received by an antenna array of a receiver to betaken into account.

With reference to FIG. 2, an aspect of the present invention proposes tosimultaneously process the spatial filtering and the temporal filteringof the plurality of radio signals received by an antenna arraycomprising at least two antennas A1, A2. The antennas A1, A2respectively receive a plurality of signals X1, X2 corresponding to oneemitted FM radio signal. After acquisition via the input stages FE1,FE2, the received signals are filtered from the spatial and temporalstandpoint by way of a dedicated stage H, the output of which is arecombined signal Y_(n) that is intended to be played.

Thus, the filtered and recomposed signal after implementation of aniterative adaptation algorithm, in particular a CMA algorithm, iswritten:

$y_{n} = {{\left( \overset{\_}{H} \right)^{T}X} = {\begin{bmatrix}{\overset{\_}{H}}_{1}^{T} \\{\overset{\_}{H}}_{2}^{T}\end{bmatrix}\left\lbrack {X_{1}\mspace{14mu} X_{2}} \right\rbrack}}$

where X₁=[x_(1,n-K+1) . . . x_(1,n)] and X₂=[x_(2,n-K+1) . . . x_(2,n)]represent the last K signals received by the antennas A1, A2; H₁ and H₂are matrices the complex components of which represent weights to beapplied to said received signals in order to ensure the solution of thespatial and temporal diversity system.

To eliminate redundant parameters, the above equation may be rewrittenso as to separate linear combinations from the spatial point of view andfrom the temporal point of view. Thus, by choosing to carry out thespatial filtering first, the following is obtained:

y _(n)=G_(1,n) ^(s) [( W _(n) ^(t) )^(T) X _(1,n)]+G_(2,n) ^(s) [( W_(n) ^(t) )^(T) X _(2,n) ^(t)]

In other words, it will be clear from FIG. 2, given that the matrices H₁and H₂ are made up of a spatial component and of a temporal component,that the recombined signal is written:

y _(n)=( W _(n) ^(t) )^(T)[ G _(1,n) ^(s) X _(1,n)+G_(2,n) ^(s) X_(2,n)]

where W_(n) ^(t) is the matrix which components have complex weightscorresponding to the components of an impulse response filter to beimplemented for the temporal filtering; G_(1,n) ^(s) and G_(2,n) ^(s)are the scalars the components of which are complex weightscorresponding to the components of a filter to be implemented for thespatial filtering; X_(1,n) and X_(2,n) are complex vectors correspondingto the signals received by two antennas A1, A2; and “^(T)” is thenotation for the transpose of the matrix.

For a K-coefficient impulse response filter, at the time n, the complexmatrix W_(n) ^(t) is written:

W _(n) ^(t)=[w _(0,n) w _(1,n) w _(2,n) . . . w _(K-1,n)]^(T)

with, in cartesian coordinates: w_(k,n)=w_(k,n) ^(T)+j w_(k,n) ^(i)

The complex scalars to be implemented for the spatial filtering are fortheir part written:

G _(1,n) ^(s) =g _(1,n) ^(r) +j g _(1,n) ^(i) , G _(2,n) ^(s) =g _(2,n)^(r) +j g _(2,n) ^(i)

In the same way, the complex vectors corresponding to the signalsreceived by the two antennas A1, A2 are respectively written:

${X_{1,n} = \begin{bmatrix}x_{1,n} \\x_{1,{n - 1}} \\x_{1,{n - 2}} \\\vdots \\x_{1,{n - K + 1}}\end{bmatrix}},{X_{2,n} = \begin{bmatrix}x_{2,n} \\x_{2,{n - 1}} \\x_{2,{n - 2}} \\\vdots \\x_{2,{n - K + 1}}\end{bmatrix}}$

The following expression for the recombined signal is obtained therefrom:

$y_{n} = {\sum\limits_{k = 0}^{K - 1}{\overset{\_}{w_{k,n}^{r} + {Jw}_{k,n}^{i}}\left( {{\overset{\_}{g_{1,n}^{r} + {jg}_{1,n}^{i}}x_{1,{n - k}}} + {\overset{\_}{g_{2,n}^{r} + {jg}_{2,n}^{i}}x_{2,{n - k}}}} \right)}}$

An iterative adaptive algorithm, in particular a CMA algorithm, is thenimplemented to determine the complex components of W_(n) ^(t), G_(1,n)^(s), G_(2,n) ^(s) allowing the following cost function to be minimized:

J _(CMA) =E{(|y _(n) |−R)²}

It will be noted that, in the present description, only a CMA algorithmof (2, 1) type is envisioned, but any other type of adaptive algorithm,in particular any other type of CMA algorithm, could equally well beimplemented.

The aforementioned cost function is minimized by means of theinstantaneous gradient technique:

$\begin{matrix}{{\nabla J_{CMA}} = {2\left( {{y_{n}} - R} \right){\nabla{y_{n}}}}} \\{= {2\left( {{y_{n}} - R} \right){\nabla\left( {y_{n}{\overset{\_}{y}}_{n}} \right)^{1/2}}}} \\{= {\left( {{y_{n}} - R} \right)\frac{1}{y_{n}}\left( {{y_{n}{\nabla\; {\overset{\_}{y}}_{n}}} + {{\overset{\_}{y}}_{n}{\nabla y_{n}}}} \right)}}\end{matrix}$

namely:

${\nabla y_{n}} = {\begin{bmatrix}\frac{\partial y_{n}}{\partial W_{n}^{t}} \\\frac{\partial y_{n}}{\partial G_{1,n}^{s}} \\\frac{\partial y_{n}}{\partial G_{2,n}^{s}}\end{bmatrix} = {\begin{bmatrix}\left\{ \begin{matrix}\frac{\partial y_{n}}{\partial w_{0,n}} \\\vdots \\\frac{\partial y_{n}}{\partial w_{k,n}} \\\vdots \\\frac{\partial y_{n}}{\partial w_{{K - 1},n}}\end{matrix} \right. \\\left\{ \begin{matrix}\frac{\partial y_{n}}{\partial g_{1,n}^{r}} \\\frac{\partial y_{n}}{\partial g_{1,n}^{i}}\end{matrix} \right. \\\left\{ \begin{matrix}\frac{\partial y_{n}}{\partial g_{2,n}^{r}} \\\frac{\partial y_{n}}{\partial g_{2,n}^{i}}\end{matrix} \right.\end{bmatrix} = {\begin{bmatrix}\left\{ \begin{matrix}\vdots \\{{\overset{\_}{G_{1,n}^{s}}x_{1,{n - k}}} + {\overset{\_}{G_{2,n}^{s}}x_{2,{n - k}}}} \\{- {j\left( {{\overset{\_}{G_{1,n}^{s}}x_{1,{n - k}}} + {\overset{\_}{G_{2,n}^{s}}x_{2,{n - k}}}} \right)}} \\\vdots\end{matrix} \right. \\\left\{ \begin{matrix}{\left( \overset{\_}{W_{n}^{t}} \right)^{T}X_{1,n}} \\{{- {j\left( \overset{\_}{W_{n}^{t}} \right)}^{T}}X_{1,n}}\end{matrix} \right. \\\left\{ \begin{matrix}{\left( \overset{\_}{W_{n}^{t}} \right)^{T}X_{2,n}} \\{{- {j\left( \overset{\_}{W_{n}^{t}} \right)}^{T}}X_{2,n}}\end{matrix} \right.\end{bmatrix} = \mspace{14mu} \mspace{79mu} {{{and}\mspace{14mu} {\nabla\overset{\_}{y_{n}}}} = \overset{\_}{\nabla_{y_{n}}}}}}}$

The cost function is then written:

${\nabla J_{CMA}} = {2\; \frac{{y_{n}} - R}{y_{n}}{\overset{\_}{y_{n}}\begin{bmatrix}{{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \\{\left( \overset{\_}{W_{n}^{t}} \right)^{T}X_{1,n}} \\{\left( \overset{\_}{W_{n}^{t}} \right)^{T}X_{2,n}}\end{bmatrix}}}$

and the complex components for the spatial and temporal filtering ofreceived signals are updated using the following equations:

$\quad\left\{ \begin{matrix}{W_{n + 1}^{t} = {W_{n}^{t} - {\mu_{W}\frac{{y_{n}} - R}{y_{n}}{\overset{\_}{y_{n}}\left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}}}} \\{G_{1,{n + 1}}^{s} = {G_{1,n}^{s} - {\mu_{G\; 1}\frac{{y_{n}} - R}{y_{n}}{\overset{\_}{y_{n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}}}} \\{G_{2,{n + 1}}^{s} = {G_{2,n}^{s} - {\mu_{G\; 2}\frac{{y_{n}} - R}{y_{n}}{\overset{\_}{y_{n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}}}}\end{matrix} \right.$

Thus, there is a correlation between the coefficients of the spatialfiltering and those of the temporal filtering. Specifically, the updateof the components of G_(1,n) ^(s), G_(2,n) ^(s) depend on W_(n) ^(t),and vice versa.

Thus, the implemented iterative adaptation algorithm, in particular theCMA algorithm, converges more rapidly and above all on more stablesolutions.

According to one preferred embodiment, an even stronger correlationbetween the components of the scalars used for the spatial filtering andthe components of the impulse response filter implemented for thetemporal filtering may be introduced.

Starting with the equation issued from FIG. 2, according to which, itwill be recalled:

y _(n)=( W _(n) ^(t) )^(T)[ G _(1,n) ^(s) X _(1,n)+ G _(2,n) ^(s) X_(2,n)]

where w_(n) ^(t) is the matrix which components have complex weightscorresponding to the components of an impulse response filter to beimplemented for the temporal filtering; G_(1,n) ^(s) and G_(2,n) ^(s)are the scalars the components of which are complex weightscorresponding to the components of a filter to be implemented for thespatial filtering; X_(1,n) and X_(2,n) are complex vectors correspondingto the signals received by two antennas A1, A2; and “^(T)” is thenotation for the transpose of the matrix.

As already indicated, for a K-coefficient impulse response filter, atthe time n, the complex matrix W_(n) ^(t) is written:

W _(n) ^(t)=[w _(0,n) w _(1,n) w _(2,n) . . . w _(K-1,n)]^(T).

In polar coordinates, w_(k,n)=a_(k,n)e^(−jθ) ^(k,n) .

Thus, W_(n) ^(t)=A_(n) ^(t)ºe^(−jθ) _(n) ^(t), with:

A _(n) ^(t)=[a _(o,n) a _(1,n) a _(2,n) . . . a _(K-1,n)]^(T)

θ_(n) ^(t)=[e ^(−jθ) ^(0,n) e ^(−jθ) ^(1,n) e ^(−jθ) ^(2,n) . . . e^(−jθ) ^(K-1,n) ]^(T)

In the same way, the scalars Gf_(x) and for their part also beingcomplex, are able to be expressed in polar coordinates. Thus:

G _(1,n) ^(s) =b _(1,n) e ^(−jφ) ^(1,n) and G _(2,n) ^(s) =b _(2,n) e^(−jφ) ^(2,n)

It will be recalled that the complex vectors corresponding to thesignals received by the two antennas A1, A2 are respectively written:

${X_{1,n} = {{\begin{bmatrix}x_{1,n} \\x_{1,{n - 1}} \\x_{1,{n - 2}} \\\vdots \\x_{1,{n - K + 1}}\end{bmatrix}\mspace{14mu} {and}\mspace{14mu} X_{2,n}} = \begin{bmatrix}x_{2,n} \\x_{2,{n - 1}} \\x_{2,{n - 2}} \\\vdots \\x_{2,{n - K + 1}}\end{bmatrix}}}\mspace{11mu}$

The following expression for the recombined signal is obtained therefrom:

$y_{n} = {\sum\limits_{k = 0}^{K - 1}{a_{k,n}\mspace{14mu} {e^{j\; \theta_{k,n}}\left( {{b_{1,n}\mspace{14mu} e^{j\; \phi_{1,n}}\mspace{14mu} x_{1,{n - k}}} + {b_{2,n}\mspace{14mu} e^{j\; \phi_{2,n}}\mspace{14mu} x_{2,{n - k}}}} \right)}}}$

Thus, as in the preceding embodiment, an iterative adaptive algorithm,such as a CMA algorithm, is implemented to determine the complexcomponents of W_(n) ^(t), G_(1,n) ^(s), G_(2,n) ^(s) allowing thefollowing cost function to be minimized:

J _(CMA) =E{(y _(n) |−R)²}

It will again be noted that, in the present description, only a CMAalgorithm of (2, 1) type is envisioned, but any other type of adaptivealgorithm, in particular any other type of CMA algorithm, could equallywell be implemented.

The aforementioned cost function is minimized by means of theinstantaneous gradient technique:

$\begin{matrix}{{\nabla J_{CMA}} = {2\left( {{y_{n}} - R} \right){\nabla{y_{n}}}}} \\{= {2\left( {{y_{n}} - R} \right){\nabla\left( {y_{n}{\overset{\_}{y}}_{n}} \right)^{1/2}}}} \\{= {\left( {{y_{n}} - R} \right)\frac{1}{y_{n}}\left( {{y_{n}{\nabla\; {\overset{\_}{y}}_{n}}} + {{\overset{\_}{y}}_{n}{\nabla y_{n}}}} \right)}}\end{matrix}$

Namely, this time round:

${\nabla y_{n}} = {\begin{bmatrix}\frac{\partial y_{n}}{\partial W_{n}^{t}} \\\frac{\partial y_{n}}{\partial G_{1,n}^{s}} \\\frac{\partial y_{n}}{\partial G_{2,n}^{s}}\end{bmatrix} = {\quad{\begin{bmatrix}\frac{\partial y_{n}}{\partial A_{n}^{t}} \\\frac{\partial y_{n}}{\partial\theta_{n}^{t}} \\\frac{\partial y_{n}}{\partial b_{1,n}} \\\frac{\partial y_{n}}{\partial\phi_{1,n}} \\\frac{\partial y_{n}}{\partial b_{2,n}} \\\frac{\partial y_{n}}{\partial\phi_{2,n}}\end{bmatrix} = {\begin{bmatrix}\begin{matrix}\vdots \\{e^{j\; \theta_{k,n}}\left( {{\overset{\_}{G_{1,n}^{s}}x_{1,{n - k}}} + {\overset{\_}{G_{1,n}^{s}}x_{2,{n - k}}}} \right)} \\\vdots \\{j\mspace{14mu} a_{k,n}\mspace{20mu} {e^{j\; \theta_{k,n}}\left( {{\overset{\_}{G_{1,n}^{s}}x_{1,{n - k}}} + {\overset{\_}{G_{1,n}^{s}}x_{2,{n - k}}}} \right)}}\end{matrix} \\\vdots \\{e^{j\; \phi_{1,n}}\mspace{11mu} \left( \overset{\_}{W_{n}^{t}} \right)^{T}X_{1,n}} \\{j\mspace{14mu} b_{1,n}\mspace{14mu} e^{j\; \phi_{1,n}}\mspace{11mu} \left( \overset{\_}{W_{n}^{t}} \right)^{T}X_{1,n}} \\{e^{j\; \phi_{2,n}}\mspace{11mu} \left( \overset{\_}{W_{n}^{t}} \right)^{T}X_{2,n}} \\{j\mspace{14mu} b_{2,n}\mspace{14mu} e^{j\; \phi_{2,n}}\mspace{11mu} \left( \overset{\_}{W_{n}^{t}} \right)^{T}X_{2,n}}\end{bmatrix} = \mspace{14mu} \mspace{79mu} {{{and}\mspace{14mu} {\nabla\overset{\_}{y_{n}}}} = \overset{\_}{\nabla_{y_{n}}}}}}}}$

Substitution of these terms in the cost function expressed above gives:

${\nabla J_{CMA}} = {2\; {\frac{{y_{n}} - R}{y_{n}}\begin{bmatrix}{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{11mu} {A_{n}^{t}\; \circ \; e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack}} \\{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{1,n}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack}} \\{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{2,n}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack}}\end{bmatrix}}}$

and the complex components for the spatial and temporal filtering ofreceived signals are updated using the following equations:

$\left\{ {{\begin{matrix}{A_{n + 1}^{t} = {A_{n}^{t} - {\mu_{A}\; \frac{{y_{n}} - R}{y_{n}}\; {{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack}}}} \\{\theta_{n + 1}^{t} = {\theta_{n}^{t} + {\mu_{\theta}\mspace{11mu} \frac{{y_{n}} - R}{y_{n}}\; {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{11mu} {A_{n}^{t}\; \circ e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack}}}} \\{b_{1,{n + 1}} = {b_{1,n} - {\mu_{b\; 1}\; \frac{{y_{n}} - R}{y_{n}}\; {{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack}}}} \\{\phi_{1,{n + 1}} = {\phi_{1,n} + {\mu_{\phi \; 1}\; \frac{{y_{n}} - R}{y_{n}}\; {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{1,n}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack}}}} \\{b_{2,{n + 1}} = {b_{2,n} - {\mu_{b\; 2}\; \frac{{y_{n}} - R}{y_{n}}\; {{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack}}}}\end{matrix}\phi_{2,{n + 1}}} = {\phi_{2,n} + {\mu_{\phi 2}\; \frac{{y_{n}} - R}{y_{n}}\; {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{2,n}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack}}}} \right.$

The strong interdependency between the real and imaginary parts of thecomplex weights to be determined will be evident from these formulae.

The implementation of iterative adaptation algorithms on these formulae,in particular CMA algorithms, with the constraint of minimizing the costfunction described above, thus converges more efficiently than in theprior art. Specifically, the spatial and temporal correlationsintroduced above induce an interdependency in the update of thecoefficients, decreasing the number of degrees of freedom, unlike CMAalgorithms such as implemented in the prior art, with which thecoefficients of the complex weights are independent linear cartesians.

By virtue of an aspect of the invention, the CMA algorithms converge toa smaller subset of solutions, said subset being included in the set ofpossible solutions of the CMA algorithms such as implemented in theprior art.

The implementation of the method according to an aspect of the inventiontherefore allows secondary signals produced by the multi-path effect tobe removed with a better stability than in the prior art.

It will furthermore be noted that an aspect of the present invention isnot limited to the embodiment described above, making recourse to CMAalgorithms, and has variants that will appear obvious to those skilledin the art; in particular, other types of iterative algorithms may beimplemented.

1. A method for decreasing multi-path interference, for implementationthereof in a vehicle radio receiver, said radio receiver being intendedto receive an emitted radio signal and comprising at least two radioreception antennas that each receive a plurality of radio signalscorresponding to said emitted radio signal, each of said plurality ofsignals received by each of said antennas being composed of time-shiftedradio signals resulting from a multi-path effect, said plurality ofradio signals being combined to deliver a combined radio signal y_(n) tobe played, with y_(n)=W_(n) ^(T)[G_(1,n) ^(S), X_(1,n)+G_(2,n) ^(S),X_(2,n)] at the time n, where X₁ is a vector the components of whichcorrespond to a plurality of signals received by a first antenna,expressed in complex baseband, X₂ is a vector the components of whichcorrespond to the plurality of signals received by a second antenna,expressed in complex baseband, G_(1,n) ^(S) and G_(2,n) ^(S) are scalarsthe components of which are the complex weights of a spatial filter andW_(n) ^(T) is the transpose matrix of a vector the components of whichare the complex weights of a temporal filter, said method comprising:the implementation of an iterative adaption algorithm to determine saidcomplex weights of the spatial filter and said complex weights of thetemporal filter, wherein the respective variations in the components ofthe matrix the components of which form the complex weights of thetemporal filter and in the components of the scalars the components ofwhich form the complex weights of a spatial filter are written:$\begin{matrix}{W_{n + 1}^{t} = {W_{n}^{t} - {\mu_{W}\mspace{14mu} \frac{{y_{n}} - R}{y_{n}}{\overset{\_}{y_{n}}\left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}}}} \\{G_{1,{n + 1}}^{s} = {G_{1,n}^{s} - {\mu_{G\; 1}\mspace{14mu} \frac{{y_{n}} - R}{y_{n}}{\overset{\_}{y_{n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}}}} \\{G_{2,{n + 1}}^{s} = {G_{2,n}^{s} - {\mu_{G\; 2}\mspace{14mu} \frac{{y_{n}} - R}{y_{n}}{\overset{\_}{y_{n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}}}}\end{matrix}$ where μ_(W), μ_(G1) and μ_(G2) are iterative steps chosenfor the update of the gains and phases of each of the complex weights.2. The method as claimed in claim 1, wherein the iterative adaptationalgorithm is configured to minimize a cost function J such thatJ=E{|y _(n) |−R)²} where R is a constant to be determined, correspondingto the constant modulus of the combined signal y_(n).
 3. The method asclaimed in claim 2, wherein said iterative adaptation algorithm is aconstant modulus adaptation algorithm configured to minimize the costfunction.
 4. The method as claimed in claim 1, further comprisingintroducing a correlation between said complex weights of the temporalfilter and said complex weights of the spatial filter, said correlationbeing dependent on the time shift between said plurality of radiosignals received by said at least two antennas, by the expression ofsaid complex weights in polar coordinates, so that the instantaneousgradient of the cost function is written:${\nabla J} = {2{\frac{{y_{n}} - R}{y_{n}}\begin{bmatrix}{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{11mu} {A_{n}^{t}\; \circ \; e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack}} \\{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{1,n}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack}} \\{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{2,n}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack}}\end{bmatrix}}}$ with:W_(n)^(t) = A_(n)^(t) ∘ e^(−j θ_(n)^(t)),  with:A_(n)^(t) = [a_(0, n)  a_(1, n)  a_(2, n)  . . .  a_(K − 1, n)]^(T)θ_(n)^(t) = [e^(−j θ_(0, n))  e^(−j θ_(1, n))  e^(−j θ_(2, n))  . . .  e^(−j θ_(K − 1, n))]^(T), and:G_(1, n)^(s) = b_(1, n)e^(−j ϕ_(1, n))G_(2, n)^(s) = b_(2, n)e^(−j ϕ_(2, n)) so as to incorporate aninterdependence between the real and imaginary parts of said complexweights.
 5. The method as claimed in claim 4, wherein the respectivevariations in the components of the matrix the components of which formthe complex weights of the temporal filter and in the components of thescalars the components of which form the complex weights of a spatialfilter are written:$A_{n + 1}^{t} = {A_{n}^{t} - {\mu_{A}\frac{{y_{n}} - R}{y_{n}}{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack}}}$$\theta_{n + 1}^{t} = {\theta_{n}^{t} + {\mu_{\theta}\frac{{y_{n}} - R}{y_{n}}{{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{11mu} {A_{n}^{t}\; \circ \; e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack}}}$$b_{1,{n + 1}} = {b_{1,n} - {\mu_{b\; 1}\; \frac{{y_{n}} - R}{y_{n}}\; {{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack}}}$$\phi_{1,{n + 1}} = {\phi_{1,n} + {\mu_{\phi 1}\frac{{y_{n}} - R}{y_{n}}\; {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{1,n}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack}}}$$b_{2,{n + 1}} = {b_{2,n} - {\mu_{2,n}\frac{{y_{n}} - R}{y_{n}}\; {{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack}}}$$\phi_{2,{n + 1}} = {\phi_{2,n} + {\mu_{\phi 2}\frac{{y_{n}} - R}{y_{n}}\; {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{2,n}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack}}}$where μ_(A), A_(θ), μ_(b1), μ_(b2), μ_(φ1), μ_(φ2) are iterative stepschosen for the update of the gains and phases of each of the complexweights, and the operator “^(a)” is defined as carrying out themultiplication of two vectors, component by component, the resultantbeing a vector.
 6. The method as claimed in claim 1, wherein thetemporal filter is an impulse response filter.
 7. A radio receivercomprising a microcontroller configured to implement the method asclaimed in claim
 1. 8. A motor vehicle comprising a radio receiver asclaimed in claim
 7. 9. The method as claimed in claim 2, furthercomprising introducing a correlation between said complex weights of thetemporal filter and said complex weights of the spatial filter, saidcorrelation being dependent on the time shift between said plurality ofradio signals received by said at least two antennas, by the expressionof said complex weights in polar coordinates, so that the instantaneousgradient of the cost function is written:${\nabla J} = {2{\frac{{y_{n}} - R}{y_{n}}\begin{bmatrix}{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{11mu} {A_{n}^{t}\; \circ \; e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack}} \\{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{1,n}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack}} \\{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{2,n}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack}}\end{bmatrix}}}$ with:W_(n)^(t) = A_(n)^(t) ∘ e^(−j θ_(n)^(t)),  with:A_(n)^(t) = [a_(0, n)  a_(1, n)  a_(2, n)  . . .  a_(K − 1, n)]^(T)θ_(n)^(t) = [e^(−j θ_(0, n))  e^(−j θ_(1, n))  e^(−j θ_(2, n))  . . .  e^(−j θ_(K − 1, n))]^(T), and:G_(1, n)^(s) = b_(1, n)e^(−j ϕ_(1, n))G_(2, n)^(s) = b_(2, n)e^(−j ϕ_(2, n)) so as to incorporate aninterdependence between the real and imaginary parts of said complexweights.
 10. The method as claimed in claim 3, further comprisingintroducing a correlation between said complex weights of the temporalfilter and said complex weights of the spatial filter, said correlationbeing dependent on the time shift between said plurality of radiosignals received by said at least two antennas, by the expression ofsaid complex weights in polar coordinates, so that the instantaneousgradient of the cost function is written:${\nabla J_{\;}} = {2{\frac{{y_{n}} - R}{y_{n}}\begin{bmatrix}{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{11mu} {A_{n}^{t}\; \circ \; e^{j\; \theta_{n}^{t}} \circ \left( {{\overset{\_}{G_{1,n}^{s}}X_{1,n}} + {\overset{\_}{G_{2,n}^{s}}X_{2,n}}} \right)}} \right\rbrack}} \\{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{1,n}\mspace{14mu} {e^{j\; \phi_{1,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{1,n}} \right\rbrack}} \\{{Re}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack} \\{- {{Im}\left\lbrack {\overset{\_}{y_{n}}\mspace{14mu} b_{2,n}\mspace{14mu} {e^{j\; \phi_{2,n}}\left( \overset{\_}{W_{n}^{t}} \right)}^{T}X_{2,n}} \right\rbrack}}\end{bmatrix}}}$ with:W_(n)^(t) = A_(n)^(t) ∘ e^(−j θ_(n)^(t)),  with:A_(n)^(t) = [a_(0, n)  a_(1, n)  a_(2, n)  . . .  a_(K − 1, n)]^(T)θ_(n)^(t) = [e^(−j θ_(0, n))  e^(−j θ_(1, n))  e^(−j θ_(2, n))  . . .  e^(−j θ_(K − 1, n))]^(T), and:G_(1, n)^(s) = b_(1, n)e^(−j ϕ_(1, n))G_(2, n)^(s) = b_(2, n)e^(−j ϕ_(2, n)) so as to incorporate aninterdependence between the real and imaginary parts of said complexweights.